## Inverse Matrix of Positive-Definite Symmetric Matrix is Positive-Definite

## Problem 397

Suppose $A$ is a positive definite symmetric $n\times n$ matrix.

**(a)** Prove that $A$ is invertible.

**(b)** Prove that $A^{-1}$ is symmetric.

**(c)** Prove that $A^{-1}$ is positive-definite.

(*MIT, Linear Algebra Exam Problem*)

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